Announcements
Today • Review membrane potential • What establishes the ion distributions? • What confers selective permeability? • Ionic basis of membrane potential Next Lectures • Action Potentials
Membrane Potential • Inside of cell is negative compared to outside • Depends on: • High concentration K+ inside • Selective permeability of membrane
What causes the different ion distributions in cells? • Passive distribution – Donnan equilibrium • Active Transport
I I II II Passive distribution – Donnan equilibrium • The ratio of positively charged permeable ions equals the ratio of negatively charged permeable ions Start Equilibrium K+ [K+] = [K+] Cl- [Cl-] = [Cl-]
Donnan Equilibrium • Mathematically expressed: • Another way of saying the number of positive charges must equal the number of negative charges on each side of the membrane
I I II II Passive Distribution • BUT, in real cells there are a large number of negatively charged, impermeable molecules (proteins, nucleic acids, other ions) • call them A- Start Equilibrium A- A- [K+] > [K+] K+ Cl- [Cl-] < [Cl-]
I II Passive Distribution Equilibrium [K+]I = [A-]I + [Cl-]I A- [K+]II = [Cl-]II [K+] > [K+] [Cl-] < [Cl-] If [A-]Iis large, [K+]I must also be large +’ve = -’ve +’ve = -’ve space-charge neutrality
The presence of impermeable negatively charged molecules requires more positively charged molecules inside the cell.
Donnan Equilibrium Example Initial Concentrations I II A- = 0 K+ = 150 Cl- = 150 A- = 100 K+ = 150 Cl- = 50 Are these ions in electrochemical equilibrium? No, EK+ = 0 mV ECl-= -27 mV
Let X be the amount of K+ and Cl- that moves Solve for X, 7500 + 200X + X2 = 22500 - 300X + X2 X=30
Final Concentrations I II A- = 0 K+ = 120 Cl- = 120 A- = 100 K+ = 180 Cl- = 80 space-charge neutrality Are these ions in electrochemical equilibrium? Yes, EK+ = -10 mV ECl-= -10 mV
What causes the different ion distributions in cells? • Passive distribution – Donnan equilibrium • Active Transport
Active Transport • ATP-powered pumps • Proteins that are capable of pumping ions from one side of the cell membrane to the other • Use energy
Active Transport • Na+ - K+ pump 2 K+ outside inside 3 Na+ ATP ADP + Pi
Active Transport • Na+ - K+ pump • 3 Na+ move out • 2 K+ move in • Hydrolyzes ATP • Maintains the concentration gradient
Active Transport • Na+ - K+ pump 2 K+ outside inside 3 Na+ • Electrogenic • net loss of 1 positive charge from inside • Inside becomes more negative • contributes a few mV to resting potential
Na+/K+ pump is required • Due to low permeability for Na+ to leak into the cell • Without pump, • Gradual accumulation of +’ve charge inside • Eventually lose the membrane potential Active ingredient in rodent poison, ouabain, poisons the Na/K pump
What causes the different ion distributions in cells? • Passive distribution – Donnan equilibrium • Active Transport
What confers selective permeability? Ion channels • Non-gated • Leakage channels • Open at rest – allow K+ to flow out along its concentration gradient K+
Membrane Potential Summary • Selective permeability • Ion channel – K+ leak channel • Unequal distribution of ions • Passive distribution (Donnan) • Active transport – Na+/K+ pump • The equilibrium potential of each ion is described by the Nernst equation • The total membrane potential is described by the Goldman equation
Ionic basis of membrane potential
Mammalian Cell Equilibrium (Nernst) Potential Inside (mM) Outside (mM)
Is the resting membrane potential controlled by one ion, or several? • Do an experiment • Measure membrane potential (Vm) of a cell • Change extracellular concentration of an ion in the bathing solution • If Vm really depends on Eion than Vm should change as Eion changes
Resting potential Measuring Membrane Potential amplifier microelectrode Reference electrode 0 mV cell -80 mV time
Expt #1vary extracellular Na Assume [Na]in = 10 mM [Na]out prediction
1 2 5 10 20 50 100 200 40 20 0 -20 Prediction of ENa From Nernst equation -40 Membrane Potential (mV) -60 -80 -100 Measured Vm -120 External Na+ concentration (mM)
Therefore, • Conclude that Vm does not follow ENa
Expt #2vary extracellular K • Assume intracellular [K] = 140 mM Extracell [K] prediction
Deviation at low [K+] due to slight permeability of Na+ 1 2 5 10 20 50 100 200 0 -20 Prediction of EK From Nernst equation -40 Membrane Potential (mV) -60 -80 -100 Measured Vm -120 External K+ concentration (mM)
Therefore, the resting membrane potential (Vm) is very close to the equilibrium potential for K+ (EK)
Summary • At rest PK>>PNa, PCl, PCa • Therefore, at rest, the membrane potential is close to EK • In general, the membrane potential will be dominated by the equilibrium (Nernst) potential of the most permeable ion
Sample Question At rest Vm of this typical cell is -75 mV. What would Vm be if PNa >> Pk,PCl? K = 140 Na = 10 Cl = 30 K = 5 Na = 145 Cl = 110 Answer: Calculate ENa using Nernst equation. Assume Vm ENa = +67 mV
The resting membrane potential is the basis for all electrical signaling • Next Lecture: Action Potentials
